Truncated Dodecahedron

This function calculates various properties of a truncated dodecahedron. A truncated dodecahedron is created by cutting off the corners of a dodecahedron so that all edges are the same length. It is a polyhedron with 32 sides, 90 edges and 60 vertices. They form 20 equilateral triangles, 12 regular decagons.

To perform the calculation, select the property you know and enter its value. Then click on the 'Calculate' button.

Truncated Dodecahedron calculator  Input Delete Entry Edge length Volume Surface Outer radius Midsphere radius Decimal places 0 1 2 3 4 6  Results Edge lengtha VolumeV Surface areaS Outer radiusrc Midsphere radius rm

Formulas for truncated Dodecahedron

Volume

\(\displaystyle V=\frac{5 · a^3 · (99+47 ·\sqrt{5}}{12}\)

\(\displaystyle a= \sqrt[3]{ \frac{12 · V }{5·(99 + 47 ·\sqrt{5})}} \)

Surface area

\(\displaystyle S= 5 · a^2 · (\sqrt{3}+6·\sqrt{5+2·\sqrt{5}})\)

\(\displaystyle a= \sqrt{ \frac{S}{5 ·(\sqrt{3}+6·\sqrt{5+2·\sqrt{5})}}} \)

Outer radius

\(\displaystyle rc=\frac{a· \sqrt{74+30· \sqrt{5}}}{4}\)

\(\displaystyle a=\frac{4·rc}{(74+30· \sqrt{5})}\)

Midsphere radius

\(\displaystyle rm=\frac{a · (5+3·\sqrt{5})}{4} \)

\(\displaystyle a=\frac{4 · rm}{5+3·\sqrt{5}} \)